def __init__(self, n, R, names):
"""
EXAMPLES::
sage: AffineSpace(3, Zp(5), 'y')
Affine Space of dimension 3 over 5-adic Ring with capped relative precision 20
"""
AmbientSpace.__init__(self, n, R)
self._assign_names(names)
AffineScheme.__init__(self, self.coordinate_ring(), R)
def __init__(self, n, R, names):
"""
EXAMPLES::
sage: AffineSpace(3, Zp(5), 'y')
Affine Space of dimension 3 over 5-adic Ring with capped relative precision 20
"""
AmbientSpace.__init__(self, n, R)
self._assign_names(names)
AffineScheme.__init__(self, self.coordinate_ring(), R)
def __init__(self, n, R, names, ambient_projective_space, default_embedding_index):
"""
EXAMPLES::
sage: AffineSpace(3, Zp(5), 'y')
Affine Space of dimension 3 over 5-adic Ring with capped relative precision 20
"""
AmbientSpace.__init__(self, n, R)
self._assign_names(names)
AffineScheme.__init__(self, self.coordinate_ring(), R)
index = default_embedding_index
if index is not None:
index = int(index)
self._default_embedding_index = index
self._ambient_projective_space = ambient_projective_space
def __init__(self, R, S=None):
"""
Construct the spectrum of the ring ``R``.
See :class:`Spec` for details.
EXAMPLES::
sage: Spec(ZZ)
Spectrum of Integer Ring
"""
if not is_CommutativeRing(R):
raise TypeError, "R (=%s) must be a commutative ring"%R
self.__R = R
if not S is None:
if not is_CommutativeRing(S):
raise TypeError, "S (=%s) must be a commutative ring"%S
try:
S.hom(R)
except TypeError:
raise ValueError, "There must be a natural map S --> R, but S = %s and R = %s"%(S,R)
AffineScheme.__init__(self, S)
def __init__(self, R, S=None):
"""
Construct the spectrum of the ring ``R``.
See :class:`Spec` for details.
EXAMPLES::
sage: Spec(ZZ)
Spectrum of Integer Ring
"""
if not is_CommutativeRing(R):
raise TypeError("R (=%s) must be a commutative ring"%R)
self.__R = R
if not S is None:
if not is_CommutativeRing(S):
raise TypeError("S (=%s) must be a commutative ring"%S)
try:
S.hom(R)
except TypeError:
raise ValueError("There must be a natural map S --> R, but S = %s and R = %s"%(S,R))
AffineScheme.__init__(self, S)
